In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processe...In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processes are relevant for polymer solutions,porous industrial materials,ceramic processing,oil recovery,and fluid beds.The present tangent hyperbolic fluid flow and heat transfer model accurately predicts the shear-thinning phenomenon and describes the blood flow characteristics.Therefore,the entropy production analysis of a non-Newtonian tangent hyperbolic material flow through a vertical microchannel with a quadratic density temperature fluctuation(quadratic/nonlinear Boussinesq approximation)is performed in the present study.The impacts of the hydrodynamic flow and Newton’s thermal conditions on the flow,heat transfer,and entropy generation are analyzed.The governing nonlinear equations are solved with the spectral quasi-linearization method(SQLM).The obtained results are compared with those calculated with a finite element method and the bvp4c routine.In addition,the effects of key parameters on the velocity of the hyperbolic tangent material,the entropy generation,the temperature,and the Nusselt number are discussed.The entropy generation increases with the buoyancy force,the pressure gradient factor,the non-linear convection,and the Eckert number.The non-Newtonian fluid factor improves the magnitude of the velocity field.The power-law index of the hyperbolic fluid and the Weissenberg number are found to be favorable for increasing the temperature field.The buoyancy force caused by the nonlinear change in the fluid density versus temperature improves the thermal energy of the system.展开更多
The optimal design of heating and cooling systems must take into account heat radiation which is a non-linear process.In this study,the mixed convection in a radiative magnetohydrodynamic Eyring-Powell copperwater nan...The optimal design of heating and cooling systems must take into account heat radiation which is a non-linear process.In this study,the mixed convection in a radiative magnetohydrodynamic Eyring-Powell copperwater nanofluid over a stretching cylinder was investigated.The energy balance is modeled,taking into account the non-linear thermal radiation and a thermal slip condition.The effects of the embedded flow parameters on the fluid properties,as well as on the skin friction coefficient and heat transfer rate,are analyzed.Unlike in many existing studies,the recent spectral quasi-linearization method is used to solve the coupled nonlinear boundary-value problem.The computational result shows that increasing the nanoparticle volume fraction,thermal radiation parameter and heat generation parameter enhances temperature profile.We found that the velocity slip parameter and the fluid material parameter enhance the skin friction.A comparison of the current numerical results with existing literature for some limiting cases shows excellent agreement.展开更多
本文根据相干斑噪声的时间快变特征和非海浪纹理现象的时间缓变特征,基于交叉谱提出了一种对相干斑噪声和大尺度非海浪纹理的抑制的方法,进而结合SAR图像谱和海浪谱之间的准线性映射关系,基于SAR数据对海浪参数进行了反演。在反演过程中...本文根据相干斑噪声的时间快变特征和非海浪纹理现象的时间缓变特征,基于交叉谱提出了一种对相干斑噪声和大尺度非海浪纹理的抑制的方法,进而结合SAR图像谱和海浪谱之间的准线性映射关系,基于SAR数据对海浪参数进行了反演。在反演过程中,首先仿真分析了不同海况下准线性近似法的海浪反演能力,结果表明:风浪引起的方位向截断效应会显著影响反演精度,因此该方法在低风速时的涌浪反演精度更高。通过将基于Sentinel-1卫星2020年的波模式SAR数据的反演结果与欧洲中期天气预报中心(European Centre for Medium-Range Weather Forecasts,ECMWF)提供的再分析数据进行对比,发现高海况海浪有效波高反演结果明显偏低,而且该反演误差与风速、方位向截断波长之间存在显著相关性。为了提高有效波高的反演精度,本文进一步给出了海浪有效波高反演误差与风速、方位向截断波长之间的经验校正函数模型,结果显示,通过该模型修正后的海浪有效波高反演结果与ECMWF数据和浮标测量数据具有良好一致性。展开更多
A strategy for time-delayed feedback control optimization of quasi linear systems with random excitation is proposed. First, the stochastic averaging method is used to reduce the dimension of the state space and to de...A strategy for time-delayed feedback control optimization of quasi linear systems with random excitation is proposed. First, the stochastic averaging method is used to reduce the dimension of the state space and to derive the stationary response of the system. Secondly, the control law is assumed to be velocity feedback control with time delay and the unknown control gains are determined by the performance indices. The response of the controlled system is predicted through solving the Fokker-Plank-Kolmogorov equation associated with the averaged Ito equation. Finally, numerical examples are used to illustrate the proposed control method, and the numerical results are confirmed by Monte Carlo simulation .展开更多
The nonlinear vibrational model of a slightly curved single-walled carbon nanotube （SWCNT） resting on a Winkler-type elastic foundation is developed using nonlocal Euler- Bernoulli elastic theory. The SWCNT is assum...The nonlinear vibrational model of a slightly curved single-walled carbon nanotube （SWCNT） resting on a Winkler-type elastic foundation is developed using nonlocal Euler- Bernoulli elastic theory. The SWCNT is assumed to vibrate under an external harmonic electric force field and an analytical solution is proposed to obtain the nonlinear resonant frequencies. The results show good agreement with the numerical simulation and the obtained analytical frequency is com- pletely related to the curvature of the nanotube. Our model predicts that although the model is nonlinear in nature, the curved SWCNT could behave linearly in a certain amount of curvatures and this quasi-linear vibrational behavior of curved SWCNT is a function of aspect ratio, nonlocal parameter, and stiffness of the foundation.展开更多
This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponent whereΩ(?)RN(N(?)3)is a smooth bounded domain,0∈Ω,0(?)s<p,1<p<N,p(s):=p(N-s)/N-p is the critical Sobolev-Hardy exp...This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponent whereΩ(?)RN(N(?)3)is a smooth bounded domain,0∈Ω,0(?)s<p,1<p<N,p(s):=p(N-s)/N-p is the critical Sobolev-Hardy exponent,λ>0,p(?)r<p,p:=Np/N-p is the critical Sobolev exponent,μ>,0(?)t<p,p(?)q<p(t)=p(N-t)/N-p.The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.展开更多
The present paper is concerned with a class of quasi-linear degenerate elliptic equations.The degenerate operator arises from analysis of manifolds with singularities.The variational methods are applied here to verify...The present paper is concerned with a class of quasi-linear degenerate elliptic equations.The degenerate operator arises from analysis of manifolds with singularities.The variational methods are applied here to verify the existence of infinitely many solutions for the problem.展开更多
In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate init...In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline approximation produces at each time level a spline function which may be used to obtain the solution at any point in the range of the space variable. The proposed cubic spline method is applicable to parabolic equations having singularity. The stability analysis for diffusion- convection equation shows the unconditionally stable character of the cubic spline method. The numerical tests are performed and comparative results are provided to illustrate the usefulness of the proposed method.展开更多
文摘In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processes are relevant for polymer solutions,porous industrial materials,ceramic processing,oil recovery,and fluid beds.The present tangent hyperbolic fluid flow and heat transfer model accurately predicts the shear-thinning phenomenon and describes the blood flow characteristics.Therefore,the entropy production analysis of a non-Newtonian tangent hyperbolic material flow through a vertical microchannel with a quadratic density temperature fluctuation(quadratic/nonlinear Boussinesq approximation)is performed in the present study.The impacts of the hydrodynamic flow and Newton’s thermal conditions on the flow,heat transfer,and entropy generation are analyzed.The governing nonlinear equations are solved with the spectral quasi-linearization method(SQLM).The obtained results are compared with those calculated with a finite element method and the bvp4c routine.In addition,the effects of key parameters on the velocity of the hyperbolic tangent material,the entropy generation,the temperature,and the Nusselt number are discussed.The entropy generation increases with the buoyancy force,the pressure gradient factor,the non-linear convection,and the Eckert number.The non-Newtonian fluid factor improves the magnitude of the velocity field.The power-law index of the hyperbolic fluid and the Weissenberg number are found to be favorable for increasing the temperature field.The buoyancy force caused by the nonlinear change in the fluid density versus temperature improves the thermal energy of the system.
文摘The optimal design of heating and cooling systems must take into account heat radiation which is a non-linear process.In this study,the mixed convection in a radiative magnetohydrodynamic Eyring-Powell copperwater nanofluid over a stretching cylinder was investigated.The energy balance is modeled,taking into account the non-linear thermal radiation and a thermal slip condition.The effects of the embedded flow parameters on the fluid properties,as well as on the skin friction coefficient and heat transfer rate,are analyzed.Unlike in many existing studies,the recent spectral quasi-linearization method is used to solve the coupled nonlinear boundary-value problem.The computational result shows that increasing the nanoparticle volume fraction,thermal radiation parameter and heat generation parameter enhances temperature profile.We found that the velocity slip parameter and the fluid material parameter enhance the skin friction.A comparison of the current numerical results with existing literature for some limiting cases shows excellent agreement.
文摘本文根据相干斑噪声的时间快变特征和非海浪纹理现象的时间缓变特征,基于交叉谱提出了一种对相干斑噪声和大尺度非海浪纹理的抑制的方法,进而结合SAR图像谱和海浪谱之间的准线性映射关系,基于SAR数据对海浪参数进行了反演。在反演过程中,首先仿真分析了不同海况下准线性近似法的海浪反演能力,结果表明:风浪引起的方位向截断效应会显著影响反演精度,因此该方法在低风速时的涌浪反演精度更高。通过将基于Sentinel-1卫星2020年的波模式SAR数据的反演结果与欧洲中期天气预报中心(European Centre for Medium-Range Weather Forecasts,ECMWF)提供的再分析数据进行对比,发现高海况海浪有效波高反演结果明显偏低,而且该反演误差与风速、方位向截断波长之间存在显著相关性。为了提高有效波高的反演精度,本文进一步给出了海浪有效波高反演误差与风速、方位向截断波长之间的经验校正函数模型,结果显示,通过该模型修正后的海浪有效波高反演结果与ECMWF数据和浮标测量数据具有良好一致性。
基金the National Natural Science Foundation of China (10772159)Specialized Research Fund for the Doctoral Program of Higher Education of China (20060335125)
文摘A strategy for time-delayed feedback control optimization of quasi linear systems with random excitation is proposed. First, the stochastic averaging method is used to reduce the dimension of the state space and to derive the stationary response of the system. Secondly, the control law is assumed to be velocity feedback control with time delay and the unknown control gains are determined by the performance indices. The response of the controlled system is predicted through solving the Fokker-Plank-Kolmogorov equation associated with the averaged Ito equation. Finally, numerical examples are used to illustrate the proposed control method, and the numerical results are confirmed by Monte Carlo simulation .
文摘The nonlinear vibrational model of a slightly curved single-walled carbon nanotube （SWCNT） resting on a Winkler-type elastic foundation is developed using nonlocal Euler- Bernoulli elastic theory. The SWCNT is assumed to vibrate under an external harmonic electric force field and an analytical solution is proposed to obtain the nonlinear resonant frequencies. The results show good agreement with the numerical simulation and the obtained analytical frequency is com- pletely related to the curvature of the nanotube. Our model predicts that although the model is nonlinear in nature, the curved SWCNT could behave linearly in a certain amount of curvatures and this quasi-linear vibrational behavior of curved SWCNT is a function of aspect ratio, nonlocal parameter, and stiffness of the foundation.
基金This research is supported by the National Natural Science Foundation of China(l0171036) and the Natural Science Foundation of South-Central University For Nationalities(YZZ03001).
文摘This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponent whereΩ(?)RN(N(?)3)is a smooth bounded domain,0∈Ω,0(?)s<p,1<p<N,p(s):=p(N-s)/N-p is the critical Sobolev-Hardy exponent,λ>0,p(?)r<p,p:=Np/N-p is the critical Sobolev exponent,μ>,0(?)t<p,p(?)q<p(t)=p(N-t)/N-p.The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.
基金supported by National Natural Science Foundation of China (Grant Nos. 11771218, 11371282 and 11631011)the Fundamental Research Funds for the Central Universities
文摘The present paper is concerned with a class of quasi-linear degenerate elliptic equations.The degenerate operator arises from analysis of manifolds with singularities.The variational methods are applied here to verify the existence of infinitely many solutions for the problem.
文摘In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline approximation produces at each time level a spline function which may be used to obtain the solution at any point in the range of the space variable. The proposed cubic spline method is applicable to parabolic equations having singularity. The stability analysis for diffusion- convection equation shows the unconditionally stable character of the cubic spline method. The numerical tests are performed and comparative results are provided to illustrate the usefulness of the proposed method.
